# Circle A has a center at (5 ,2 ) and an area of 15 pi. Circle B has a center at (4 ,7 ) and an area of 80 pi. Do the circles overlap?

Feb 19, 2016

Circles do overlap.

#### Explanation:

Distance between $\left(5 , 2\right)$ and $\left(4 , 7\right)$ is given by

$\sqrt{{\left(4 - 5\right)}^{2} + {\left(7 - 2\right)}^{2}}$ i.e. $\sqrt{{\left(- 1\right)}^{2} + {5}^{2}}$ i.e. $\sqrt{26} = 5.099$

As radius of a circle is given by $\pi {r}^{2}$,

radius of circle A is $\sqrt{15} = 3.873$ and

radius of circle B is $\sqrt{80} = 8.944$

As sum of the radii of the two circles at $12.817$ is more than distance between their centers which is $5.099$, circles do overlap,